The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables
Complex Variables
2026-04-15 v1
Abstract
We obtain upper bounds for the norm of the Schwarzian derivative of convex holomorphic mappings defined on the polydisk and the unit ball in . For coordinate-wise convex mappings on the polydisk, we derive a sharp estimate extending the classical one-variable result of Chuaqui--Duren--Osgood to higher dimensions. For the Roper--Suffridge extension operator in the unit ball, we obtain an explicit bound that represents the best available estimate in this setting.
Cite
@article{arxiv.2604.12010,
title = {The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables},
author = {Rodrigo Hernández},
journal= {arXiv preprint arXiv:2604.12010},
year = {2026}
}